I'm afraid a) this is nothing new, b) not quite right, and c) of limited applicability. Taking them in reverse order, this is true for main sequence stars only, and there is a clear break in the law around one solar mass: below it, the exponent is around 1.7 or 1.8 (not your 1.5) and above it it's closer to 1.2. This has to do with the onset of convection. Finally, this has been known for a very long time - it goes back at least to the 1970's and quite probably the 1930's.

I listed above the Predicted Masses (R1.5) for all (Main Sequence) star types, and the agreement is substantial for the lot of them. Therefore, a constant exponent of 1.5 is applicable for all of them, assuming the masses & radii I cited are accurate.

Actually, I dispute both your data collection procedure which stopped at Wikipedia (and ignored the obvious point of the sun, at a radius and luminosity of the sun). Had you used more data points - and the data are out there - you would have seen that there is clearly a break in the curve.

I dispute your ability to do curve fitting, as a simple best fit returns a smaller exponent.

I also am not impressed with your scholarship, as the idea of a power-law relationship or relationships between radius and mass is many decades old.

Furthermore, if you use the larger and more complete table at Wikipedia's entry on http://en.wikipedia.org/wiki/Main_sequence" [Broken], you would find a best fit exponent of 1.3, not 1.5. You would also see that the power law doesn't fit well to the curve: the exponent changes over the course of the curve.

A best fit of 1.3 corresponds to an average polytrope of n = 1.9. This is sensible - for a completely non-convective star you expect n = 3 and for a completely convective one you expect n = 1.5.

(1) This is not new. After chasing around, I've found that these kinds of relationships were being discussed in 1907.

(2) This is not correct: using the Wikipedia table I posted, one gets an exponent of 1.3, not 1.5 and it's clear that the curve does not fit a simple power law.

(3) This is of limited applicability: it's true for main sequence stars only, even though your derivation assumes nothing about the star being on the main sequence.

I also took a look at the Wikipedia article where you say you got your table from, and was amazed to find something different than what you posted there. There are ranges for masses and radii, not single numbers. One cannot pick a number from the range to match one's theories.